...rectangle PF. PC may be equal to the rectangle PD. PA. 164. To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. 165. Two straight lines stand at right angles to each other, one...

...rectangle PF.PCmay be equal to the rectangle PD.PA. 164. To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. 165. Two straight lines stand at right angles to each other, one...

...double of the square on half the line, and of the square on the intermediate part ......... 1.9. 4. If a straight line be bisected and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double...

...is equivalent *o tht difference of their squaret / E 7, Jl E & I PROP. VI THEOR. If a straight tine be bisected, and produced to any point ; the rectangle...produced, and the part of it produced, together with th» square of half the line bisected, is equal to the square of the straight line which is made up...

...parallelogram are equal to one another. 1. Add together c\vt. 17 it; 8 19 qrs. 8 2 3 1 11.9 21 20 6 8 3. If _ straight line be bisected, and produced to any point,...by the whole line thus produced .and the part of it produeed, together with the square of half the line bisected, is equal to the square of the straight...

...shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 10. If a straight line be bisected, and produced to any...the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half...

...lines AC, CD, is equal to the rectangle contained by their sum and difference. PROPOSITION 6. THEOREM. If a straight line be bisected, and produced to any point, the rectangle cjntained by the whole line thus produced, and the part of it produced, together with the tquare on...

...another problem of the same nature, in which it is required to p^gduce a straight line AB, such that the rectangle contained by the whole line thus produced and the part produced shall be equivalent to the square of the line AB itself. Bisect AB in C ; draw the perpendicular...

...extreme and mean ratio and produced so that the part produced is equal to the smaller of the segments, the rectangle contained by the whole line thus produced and the part produced together with the square on the given line, will be equal to four times the square ou the...

...are double of the squares on AC, CD. Wherefore, if a straight line &c, QED PROPOSITION 10. THEOREM. If a straight, line be bisected, and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double...